There is indeed a cart designed specifically for what you have in mind. It’s called the Sherpa Cart and is made by a company based in Arizona (www.sherpacart.com). Their camping-specific model, imaginatively named the Camping Cart, costs $165 and looks much like a warehouse hand truck, except the wheels are taller and the cart has a large backpack-type bag that extends almost the cart’s full height. It’s made from welded steel and weighs a hefty 23 pounds. Yes, that’s anathema to most ounce-counting backpackers, but who’s counting? You’re pushing (though bear in mind that may not necessarily be good for your back, either).
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The included bags have a capacity of around 5,200 cubic inches, about the same as a large backpack, and the cart itself can hold 200 pounds (as if!). You can push or pull itwhichever suits the terrain and your comfort. This isn’t a go-anywhere cartrocky trails will flummox itbut for access to campsites that are on good trails and are moderately close to a trailhead, it’s just the ticket.
The existence of the Sherpa Cart actually raises interesting possibilities. For folks in your situation, of course, it’s perfect. Parents with infants, meanwhile, could load their camp gear on a cart, and carry a child backpack with the youngster. Hunters might find the cart useful for packing out game. And then there’s the ability to haul beer on the thingwhat, four or five full cases? The mind boggles.